Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

摘要

An H~1-Galerkin mixed finite element method (H~1MFEM) is proposed and analyzed for the fourth-order nonlinear Rosenau-Burgers equation. By introducing three auxiliary variables, the first-order system of four equations is formulated. The fully discrete scheme is studied for problem and optimal a priori error estimates for L~2 and H~1-norms for the scalar unknown, first derivative, second derivative and third derivative are obtained simultaneously.